Spherometer.



LBEGKER.

SPHEROMETER.

APPLIOATION FILED DBO. 30, 1910.

Patented Apr. 14,1914.

lnventar JOSEPH BECKER, OF WASHINGTON, DISTRICT OF COLUMBIA.

srnnnoiunrnn.

noeasoa Specification of Letters Patent.

Fatented Apr. 1 1, 1914.

Application filed December 30, 1910. Serial No. 600,003.

To all whom it may concern Be it known that I, JosnrI-r BECKER, acitizen of the United States, residing at /Vashington, in the Districtof Columbia, have invented new and useful Improvements in Spheronieters,of which the following is a specification.

My invent-ion relates to spherometers of the type having generally threerigidly connected points adapted to be rested on the spherical surfaceto be measured, While a fourth adjustable point is brought into con 7tact with the spherical surface to yield a measure which according towell established rules permits of deducting or calculating the radius ofcurvature.

In trict theory the four contacting points of a spherometer should bewithout dimension, that is, should be purely geometrical points, butthis is not possible in practice and hence there must always bepresentcertain errors due to the unavoidable imperfections of thepoints.

The object of my invention is to avoid this difficulty withoutcomplicating the comparatively simple standard spherometer formula, andto this end. my invention consists in providing each needle point of theideally perfect spherometer with a perfect concentric sphere of anydesired radius, but such that all spheres simultaneously used on thesame instrument shall be of the same radius. In speaking of any needlepoint and its corresponding sphere as concentric I mean that the sphereis formed or mounted so as to have its geometrical center coincidentwith such needle point. By this means the spherometer proper has itspoints of virtual contact located at the geometrical centers of the fourspherical feet, and these ideally perfect points of contact never cancome into contact with the real surface to be measured but only with theimaginary spherical surface that lies parallel to the real surface at adistance therefrom exactly equal to the common radius of the fourspherical feet. 1

My invention is directly applicable to the simplified three pointspherometer of the common type used by Opticians in measuring thedioptricpower of eye glasses, but as such devices are generallyincapable of yielding the precise results aimed at by my improvements 1shall illustrate my invention as applied to the standard four pointspherometer.

In the accompanying drawings, where similar reference signs refer tosimilar parts: Figure 1 is an inverted plan of one of the simplest formsof my invention; and Fig. 2 is an axial section on line 2 of Fig. 1, butshowing, in addition, a sphere in contact with the four legs as it mustbe when the measurement is taken. Figs. 3 and 4 are diagrams to showthat the theoretical basic triangle of the instrument is not changed bychanging the size of the contact spheres.

The spherometer comprises a table 10 mounted on three rigid andpreferably equidistant legs 11, 12, 13, of which 13 is concealed inFig,1 and not present in Fig. 2. The fourth or adjustable leg 14 is threadedto screw up and down through table 10, and is provided with a largegraduated head 15, the revolutions of which are measured by the aid ofthe side scale 16 which is firmly fastened to table 10. The screw 14: ispreferably made with a pitch of 1 mm. and its complete revolutions arecounted on scale 16, which is also in millimeters for this purpose.Fractions of a turn are measured by the scale on head 15 which ispreferably divided into 100. equal parts, as indicated in Fig. 2. So farthe instrument presents nothing radically new except a heavierconstruction than usual, this being permissible because of the amplesupport afiorded by the spherical feet in which the essence of theinvention resides. In accordance with my invention, therefore, the fourfeet 11, 12, 13 and 14: are provided with perfect spheres S, S, S, S,all four being of the same but any desired radius r, and having theircenters exactly coincident with the imaginary and hence geometricallyperfect points A, B, C, D of the feet. In the drawings all geometricalpoints are indicated by heavy black dots for clearness.

Let R (Fig. 2) be the radius to be meas ured, then (R-i-r) will be theradius of the sphere determined by the four geometrical points A, B, C,D. Drawing All) (Fig. 2) perpendicular to DX we have by a known theorem:

K12=DE DX whence.-

m an mann =n1r= DE in which r is always positive, regardless of the signof R; is a constant equal to fi (if the basic triangle ABC be, as

usual, equilateral) and DE is the measurement given by the micrometer14, 15, 16.

Formula (1) is substantially identical with the standard spherometerformula which will be found A Laboratory Course in Experimental Physics,by Loudon and McLennan, New York and London, 1895.

In Fig. l pointsm, y, 2 and w beingthe points of contact with thespherical surface to be measured, triangle any z will be seen to bevariable in size, according to the size and sign of R. It is identicalwith ABC for a plane surface; smaller than ABC, as in Figs.v 2 and 3,for convex surfaces; and larger than ABC for concave surfaces, as seenin Fig. 3. The different positions of a: in Figs. t and 3 aredistinguished as it, w, w, w. The triangle nag z, therefore, is veryvariable, but the triangle ABC, which alone enters into the precedingcomputation, remains absolutely invariable, and this is the feature thatsubstantially preserves the standard spherometer formula, in which AEthe sole constant of the instrument, is easily derived from the value ofAB:-BC=CA. One of the principal advantages of my instrument is thatthese distances AB, BC, CA, between centers A, B and C, are very easilymeasured by calipering the inside shortest distance (Fig. 1) betweenspheres and adding 27, or else by calipering the outside longestdistance and subtracting 21', or again it may be found by taking theaverage of these two caliperings.

If the three distances turn out to be slightly unequal so that we have,say,

AB c, BC 'a, CA=?J, then their average or may without committing anygreat error be used for AB in calculating the value of AE that is is tosay,

E m+b+a 2 1 which becomes a as before stated, when given on page 11 ofin which the first factor of the denominator V is the total peripheryofthe triangle and the three following factors are the three differencesobtained by subtracting each side in turn from the sum of the other twosides.

Although there is no doubt that the sphere actually measured has aradius (Rd-7 it would be a mistake to assume that, for a given value ofB, the measure DE is a constant independent of r. According to equation(1) the value of DE may be expressed by in which AE is a constant. DE,therefore, varies not only with R, but also with '9", even if R besupposed constant. This is illustrated in Figs. 3 grams illustrating theeffects produced by substituting a larger ball foot S for the foot Sshown in Figs. 1 and 2. The effects differ according to whether thesurface to be measured is concave, as in Fig. 3, or convex, as in Fig.4. In both cases, and in general, the basic triangle ABC, as alreadyexplained, remains invariable, but is lifted into a concentric sphere.On the convex surface, Fig. 4, the lift is from A to A into a sphere ofless curvature which reduces the reading from DE to DE; and on a concavesurface, Fig. 3, the lift-is from A to A into a sphere of greatercurvature which increases the reading from DE to D E Moreover, in Fig. 1the point of contact :19 is shifted to m, and in Fig. 3 the differentpoint of contact cc is shifted to w. While contact points 00, 3 2 asthus seen vary in position, with any variation in R or r, contact pointto of the central screw 14 remains central and, therefore, screw 14 doesnot need aspherical termination at all except to permit ofmeasuringconcave surfaces and in this case any rounded end will answer.points A, B, C are, therefore, all that the theory of my inventionrequires, and these three are best made not as attachments for and 4,which are dia- The spheres on already pointed feet, but by turning eachleg and its sphere out of the solid metal. Should the three spheres usedturn out to be slightly unequal, say with radii r, r,

1 1", then their average (r+r+r) should be used for the value of r.

WVhile I have shown a micrometer screw 14c for measuring thedisplacements of the movable point D, it will be understood that anyother suitable measuring means may be used instead, as my invention isentirely independent of such measuring means.

The principal advantages of my invention are: First. Absolutetheoretical accuracy, due to absolute invariability of the basictriangle ABC, and facility of measuring the same. Second. Solidity ofconstruction, desirable in itself and as insuring accuracy. Third.Provision of almost fiat contact surfaces that will not mar or injurethe work, and that will not yield.

The facility of measuring the basic triangle ABC is especially valuablein spherometers of the Perreaux type, in which the three feet areradially adjustable to change the size of the basic triangle as setforth in vol. 49 of the Ballet in dc Za Sooz't dEnmanagement, Paris,1850 (pp. 1 15, 146; Figs. 1, 2, 3 of Plate 1136).

By referring to an article of Czapski in the Zez'zfschm'ft f'iirInstrumentenktmcle, year 1887, pp. 297 to 801, it will be seen that myinvention effectively avoids all objections that can be made to thecommon needle point spherometer as well as to the Bamberg knife edgespherometer shown in Czapskis Fig. 3, and that it can be used incombination with a well, as will be obvious on inspection of CzapskisFig. 1, for measuring the curvature of small lenses. The different usesof the well are fully explained in an article by Alfred M. Mayer intheAmen z'can J owned 0 f Science for July, 1886, third series, Vol. XXXII,pp. 61 to 69.

According to Vvinkelmann, H a/nd'bach cler Pkg silt, vol. 1, Leipzig,1908, page 100',

&

Zeiss, of Jena, constructs a very accurate spherometer having a ringwith an inner circular knife edge for convex surfaces, and an outercircular knife edge for concave surfaces. An objection to this Zeissring, however, is that it provides for a continuous and perfectlycircular line of contact, and that this condition can only be satisfiedwhen the surface whose radius of curvature is to be measured is aperfect sphere. The tripod spherometer, on the other hand, can alwaysrest solidly on the most irregular surface, and may, indeed, be used fordetecting such irregularity.

The practical value and importance of the present invention will appearon reference to the Oomptes Renders, Paris, 1911, tome 152, pp. 421%23(also prratum on page 648 of the same volume), where a description isgiven of substantially the same ball foot spherometer as independentlyinvented by Nugues, who uses accurately made ball hearing balls for thefeet. This Nugues spherometer is again referred to in the Zeitsoim'ftfair [astrumeatenlcmiclc, Berlin, 1911, p. 208.

hat I claim as my invention and desire to secure by Letters Patent is:

1. A spherometer having rigidly connected contact members composed ofrelatively large rigid spheres of the same radius, arranged so that thegeometrical centers of such spheres shall correspond to the idealgeometrical needle points of the instrument.

2. A spherometer of the tripod type, having three rigidly connected feetor cont-act members composed of relatively large rigid spheres of thesame radius, arranged so that the geometrical centers of such spheresshall correspond to the three ideal geometrical needle points of theinstrument.

In testimony whereof, I have signed my name to this specification in thepresence of two subscribing witnesses.

JOSEPH BECKER.

Witnesses:

MARY E. POW'ELL, V. E. WRIGHT.

Copies of this patent may be obtained for five cents each, by addressingthe Commissioner of Patents, Washington, D. G.

